Question

A particle starting from rest moves in a straight line with acceleration proportional to x^2, (where x i displacement). The gain of kinetic energy for any displacement is proportional to :1) x^32)x^1/23)x^2/34)x^2

Answer 1

Final Answer :
${x}^{ 3}$

Steps and Understanding :
1) Given that,

$a = k {x}^{3}$
where k is constant.

2)
$\frac{vdv}{dx} = k {x}^{2} \\ = > vdv = k {x}^{2} dx$
3) Integrate both sides from
v = 0 to v = v and x = 0 to x = x

We get,
$\frac{ {v}^{2} }{2} = \frac{k {x}^{3} }{3} \\ = > \frac{m {v}^{2} }{2} = \frac{mk {x}^{3} }{3}$
where 'm' is mass of particle.

4) Then,
Gain in Kinetic Energy = 1/2 mv^2 - 0
=mkx^3/3 -0

Hence, Gain in Kinetic Energy is proportional to
${x}^{3}$

Answer 2

Answer:

proportional to x^3

Explanation:

Dekho apun ko itna sar dard karna hi nahi

As we know change in kinectic energy equas wok done by a body

so as a is directely proportional to x^2

and work done = Force * displacement = m * a * x

so work done is propotional to acceleration and displacement i.e.

change in kinetic energy = workdone proportional to x^3

simple inta sochna hi nahi :)